Related papers: Super-Resolution of Positive Sources: the Discrete…
The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…
A trademark of nonlinear, time-dependent, convection-dominated problems is the spontaneous formation of non-smooth macro-scale features, like shock discontinuities and non-differentiable kinks, which pose a challenge for high-resolution…
To be able to resolve molecular-clusters it is crucial to access vital informations (such as, molecule density and cluster-size) that are key to understand disease progression and the underlying mechanism. Traditional single-molecule…
We analyze the fundamental resolution of incoherent optical point sources from the perspective of a quantum detection problem: deciding whether the optical field on the image plane is generated by one source or two weaker sources with…
We propose a novel method to accurately reconstruct a set of images representing a single scene from few linear multi-view measurements. Each observed image is modeled as the sum of a background image and a foreground one. The background…
Image super-resolution (SR) is a field in computer vision that focuses on reconstructing high-resolution images from the respective low-resolution image. However, super-resolution is a well-known ill-posed problem as most methods rely on…
This work deals with a regularization method enforcing solution sparsity of linear ill-posed problems by appropriate discretization in the image space. Namely, we formulate the so called least error method in an $\ell^1$ setting and perform…
Super-resolution is a machine-learning technique in image processing which generates high-resolution images from low-resolution images. Inspired by this approach, we perform a numerical experiment of quantum machine learning, which takes…
Radio-Stereometric-Analysis and x-ray fluoroscopy are radiological techniques that require dedicated software to process data. The accurate calibration of these software is therefore critical. The aim of this work is to produce a protocol…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
We investigate the problem of reconstructing n-by-n structured matrix signal X via convex programming, where each column xj is a vector of s-sparsity and all columns have the same l1-norm. The regularizer in use is matrix norm…
Superresolution fluorescence microscopy techniques beat the diffraction limit, enabling ultra-high resolution imaging in biological physics and nanoscience. In all cases that have been studied experimentally, the resolution scales inversely…
Resolving signals with closely spaced frequencies is central to applications in communications, spectroscopy and sensing. Recent results have shown that quantum sensing protocols can exhibit superresolution, the ability to discriminate…
The standard imaging algorithm for interferometric radio data, CLEAN, is optimal for point source observations, but suboptimal for diffuse emission. Recently, RESOLVE, a new Bayesian algorithm has been developed, which is ideal for extended…
This paper studies sparse super-resolution in arbitrary dimensions. More precisely, it develops a theoretical analysis of support recovery for the so-called BLASSO method, which is an off-the-grid generalisation of l1 regularization (also…
Best subset selection in linear regression is well known to be nonconvex and computationally challenging to solve, as the number of possible subsets grows rapidly with increasing dimensionality of the problem. As a result, finding the…
Restoration of digital images from their degraded measurements has always been a problem of great theoretical and practical importance in numerous applications of imaging sciences. A specific solution to the problem of image restoration is…
Spatial resolution is one of the most important specifications of an imaging system. Recent results in quantum parameter estimation theory reveal that an arbitrarily small distance between two incoherent point sources can always be…
We provide a quantitative analysis of super-resolution imaging techniques which exploit temporal fluctuations of luminosity of the sources in order to beat the Rayleigh limit. We define an operationally justified resolution gain figure of…
Locating a target is key in many applications, namely in high-stakes real-world scenarios, like detecting humans or obstacles in vehicular networks. In scenarios where precise statistics of the measurement noise are unavailable,…